{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IHDVI4L7JWIRZ43UXWDZFSJ3UX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5af0213cc385595c4dc228b6fd7b1c0a72b671bd417b7cf6e658a29439c2ab6c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-04T08:39:09Z","title_canon_sha256":"6630b63906f1ad56d5edc3432ef909f4628efd66fd4b632b92779b96c64ac2da"},"schema_version":"1.0","source":{"id":"1509.01580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01580","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01580v1","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01580","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"IHDVI4L7JWIR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IHDVI4L7JWIRZ43U","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IHDVI4L7","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:7a6f2bf043e3f04917c929748539c4628907087504b05e1f8279ba8db65db9a4","target":"graph","created_at":"2026-05-18T01:33:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\{A(t)\\}_{t \\in \\mathbb{R}}$ be a path of self-adjoint Fredholm operators in a Hilbert space $\\mathcal{H}$, joining endpoints $A_\\pm$ as $t \\to \\pm \\infty$. Computing the index of the operator $D_A= (d/d t) + A$ acting in $L^2(\\mathbb{R}; \\mathcal{H})$, where $A = \\int_{\\mathbb{R}}^{\\oplus} dt \\, A(t)$, and its relation to spectral flow along this path, has a long history. While most of the latter focuses on the case where $A(t)$ all have purely discrete spectrum, we now particularly study situations permitting essential spectra.\n  Introducing $H_1={D_A}^* D_A$ and $H_2=D_A {D_A}^*$, we c","authors_text":"Alan Carey, Fedor Sukochev, Fritz Gesztesy, Galina Levitina","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-04T08:39:09Z","title":"On the Index of a Non-Fredholm Model Operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01580","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ea1301bdcc5c4e1df7d81cd4b4af46d960a5fd0f3706f362c5c67d2611a82e08","target":"record","created_at":"2026-05-18T01:33:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5af0213cc385595c4dc228b6fd7b1c0a72b671bd417b7cf6e658a29439c2ab6c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-04T08:39:09Z","title_canon_sha256":"6630b63906f1ad56d5edc3432ef909f4628efd66fd4b632b92779b96c64ac2da"},"schema_version":"1.0","source":{"id":"1509.01580","kind":"arxiv","version":1}},"canonical_sha256":"41c754717f4d911cf374bd8792c93ba5e4f43c6a4475975c9f402f4630ca3480","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41c754717f4d911cf374bd8792c93ba5e4f43c6a4475975c9f402f4630ca3480","first_computed_at":"2026-05-18T01:33:51.109601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:51.109601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMgbGYMu3/IFMCcCG8+lI7a0+6/F2DQdrdNyYioW79nKaVi6I+tlYFsts7ZdRxh9/16344ug4OnFpIaN0/3mDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:51.110100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea1301bdcc5c4e1df7d81cd4b4af46d960a5fd0f3706f362c5c67d2611a82e08","sha256:7a6f2bf043e3f04917c929748539c4628907087504b05e1f8279ba8db65db9a4"],"state_sha256":"51f6aebbdcc540b3015f73f25ce67e0ae76e281a67a039b6c92488888dec4b8b"}